Any time I try to do anything diplomatic, such as negotiating the surrender of my enemies, I can only talk to one at a time, clearly due to the small size of the room. This leads to inconvenient problems. Such as Babylon refusing to capitulate because they are afraid of my Russian enemies. Meanwhile Russia refuses to capitulate because they are afraid of my Babylonian enemies. If only I could sit them down and calmly explain that I will crush both of them, so they don't need to be afraid of each other.

This is of course secondary to the reasoning of "we won't surrender to the guy who is currently wrecking our empire because someone else whose empire you are also wrecking might attack us." While I accept that "devil you know" is sometimes a useful concept, when one devil is actively demonstrating his ability to completely flatten you and the other is also being flattened, well let's try math:

Me > RussiaMe > Babylon

Therefore Russia cannot be any more powerful relative to Babylon than I am relative to Babylon, and the reverse. Or to put it another way, if I will kill you and I will kill him, wouldn't you rather take your chances that maybe he won't kill you?

To make it even worse, by the time they accept defeat, they are so badly crushed that there's barely any point in having them as an ally, so I might as well finish them off. Such a waste of time. Don't they understand that my Ottomans are clearly the master race and it is improper to waste the time of the superiors? Which reminds me, why doesn't Civilization have more racism? That could add a whole new level of strategy. Similar to how religion was a great way to pretend to be pious in order to better manipulate people. You know, realism.

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Actually, it does make a certain sense. In real life, it is quite common for people to be far more afraid of their closest rival rather than the top dog in the hierarchy.

Imagine a TBC-era quiet backwards WoW server, where two raiding guilds are trying to race each other for BT/Hyjal server firsts. They'd be far more concerned about their rival beating them to the punch or poaching their key players than about Nihilum doing the same.

Or take an office worker jockeying for promotion to a supervisor position. Who would she be worried more about: her coworkers trying to do the same, or the CEO of the company (who could step in and fire them all at any moment)?

If you want them to listen to you, you need to eliminate their internal rivalries by establishing a clear pecking order. So pick one side, and crush it ruthlessly. Once the math becomes "You > Russia > Babylon" or "You > Babylon > Russia", you'll find that they'll become far more reasonable.

Which reminds me, why doesn't Civilization have more racism? That could add a whole new level of strategy. Similar to how religion was a great way to pretend to be pious in order to better manipulate people. You know, realism.

Civilization still needs to sell well, and games with a realistic historical representation of racism have a notable difficulty doing that.

I see what you're saying, with the rivalries, but there are two factors to add. First off, one used to be the vassal of the other, so there is that potential order, though admittedly I have mostly destroyed the stronger power, so maybe that order is lost. Second, neither has any offensive capabilities anymore, so it's not as if either can hurt the other.